google search in header

This is my first website I’m building but I’m learning how to do things with css quickly. I have seen other posts that ask to put the WordPress search bar in the header and that works for me (though not to the right of the image; but underneath it). However, my boss has specifically requested that I put a google search bar in the header.

This (click me) is currently what the site looks like and this (click me) is what I’d like to do.

I assume this means adjusting code in the child theme’s header file. I am currently using the Wordress Google Search plugin. Here is the LINK to the site I am building (it loads slow b/c of server issues).

I’m using the Twentytwelve Theme

Thank you in advance.